Summary: Errata and Updates for volumes I,II
Vol. I.
p. 308 2.1.10 Given L < R and a R define La-1
= {r R : ra L}. If L is
a maximal left ideal in R then so is La-1
, for any a = 0 in R, and core(La-1
)
core (L).
p. 312
2.5.4 A more explicit way of viewing theorem 2.5.22. Say a ring R is special
if there is a non-nilpotent element a such that every nonzero ideal of R contains
a power of a. Prove that every prime special ring R satisfying the conditions of
theorem 2.5.22 is primitive. (Hint: The left ideal (l - ai
) is comaximal with
every nonzero two-sided ideal.) Consequently any ring R satisfying the conditions
of theorem 2.5.22 and having no nonzero nil ideals is a subdirect product of special
primitive rings. (Hint: Requires the proof of proposition 2.6.7.)
2.10.0 The following properties of a module M are equivalent: (i) M is injective;
(ii) Any map f : N E satisfies f(N) M, where M is viewed as a submodule
of its injective hull E; (iii) As in (ii), but for any essential extension E of M. Note